Questions tagged [quantum-chemistry]

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Adiabatic vs diabatic molecular surfaces

I am a bit confused about the quantum numbers in the case of diabatic potential energy curves (PEC) for diatomic molecules. Below it is a figure from this paper that I will be referring to. So as far ...
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51 views

Lagrangian of a Hydrogen Atom

So in classical mechanics, we can generally convert from the Hamiltonian to the Lagrangian and back using Legendre transformations. However, I have found this to be a bit troublesome in QM. ...
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19 views

Expectation Value of an Operator in the Projector Augmented Wave Method

I'm starting on DFT and came across this technique called PAW Wave Method for multi atoms system wave function. It is a widely employed method in DFT calculations. From the attached picture, I'm ...
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107 views

Creation and Annihilation Operators In the Hydrogen Atom

In my quantum chemistry course, we have been discussing the wavefunctions of the hydrogen atom, further, I am familiar with the idea of ladder operators from the QHO. Can we use ladder operators to ...
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21 views

Theoretical origins of optical rotation

I'm not sure if I searched this with as fine-toothed a comb as I should have, but I found nothing online. I wanted to know if someone could point me to outlets wherefrom I could learn about the ...
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2answers
55 views

Attraction and repulsion between atoms

In six east pieces Richard Feynman describes atoms as little particles that move around in perpetual motion attracting each other when they are a little distance apart but repelling upon being ...
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14 views

Momentum space Hartree-Fock overlap matrix

I was looking at Hartree-Fock studies of systems like twisted bilayer graphene, see for example: https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.031034. Here, the orbitals chosen are eigenstates ...
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34 views

Why exactly do bonds form?

From my solid state physics class I know about all the various types of bonds and the mechanisms that cause them. Let's leave the specific physics aside for now and just accept that a bond lowers the ...
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177 views

Energy level splitting in two-state systems

I was learning basic quantum mechanics using Feynman Lectures on Physics. In Chapter 8 Feynman has described ammonia inversion due to tunnelling. Feynman has first used the base states as the two ...
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28 views

Does the region inside of buckyball have a slightly negative energy density due to the casimir effect?

I was considering a buckyball floating in a vacuum. It's surface is a strongly conducting surface and so I would expect some kind of Casimir effect to apply, i.e. the wavelength of virtual photons ...
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27 views

Do the 'fine transitions' of electrons in a molecule or atom involve jumps between sublevels within a 'level', e.g. from $s$ to $d$?

Hyperfine transitions, like the (astronomically) famous 21cm line, involve just spin flips, right? And the electron jumps we first learn about in school, that release visible or near-visible photons, ...
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24 views

Does the intrinsic spin of electrons change when we excite electrons for hybridisation?

Have had been told that electrons can move from one energy level to another by transmitting or taking in energy, and do that profitably in hybridisation. I am interested in knowing how exactly do they ...
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21 views

Cross section for Hydrogen molecule formation

I have been searching for theoretical articles that calculate the hydrogen formation cross section $\sigma(H+H \rightarrow H_2)$, but I found nothing. Can anyone suggest me articles or computer ...
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8 views

Dissociation probability vs ionization probability

Suppose we have a diatomic molecule whose ionization energy is $I$ and dissociation energy is $D$ such that $I>D$. Now suppose an electron with energy $E>I>D$ collides with this molecule. ...
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20 views

Why do molecules showing a pure rotational spectra require a permanent dipole?

I understand that pure rotational spectra only exist for molecules which have a permanent dipole moment. The common explanation is "so that they can interact with the E-field of the incoming ...
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45 views

Why do molecules absorb “exact” frequencies when given a “continuous” beam of light?

This question is in the context of performing simple rotational spectroscopy on molecules, but could be extended for more general cases. In rotational (microwave or IR) spectroscopy of molecules, the ...
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47 views

Electric quadrupole allowed transitions mathematical proof

Consider the electric quadruple moment operators as follows: $Q_{20} = \frac{e}{2}(x^2+y^2-2z^2) $ $Q_{2 \pm1} = \frac{e\sqrt{6}}{2}z(x\pm iy) $ $Q_{2 \pm2} = - \frac{e\sqrt{6}}{4}(x\pm iy)^2 $ I ...
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38 views

Is a solution to the Hartree-Fock equations guaranteed to exist? Is it a Slater determinant in any basis?

My understanding is that the Hartree-Fock equations can be derived from the variational theorem as follows: The variational theorem states that for an arbitrary wavefunction $|\psi \rangle$, $\langle \...
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40 views

Why two orbitals having same phase is not a random phenomenon?

I have been reading about Molecular Orbital Theory for Chemistry. I tend to believe that when two Hydrogen atoms approach each other, whether the $1s$ orbitals are in-phase or out-phase is a random ...
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58 views

General form of Hartree-Fock potential

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ I ...
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360 views

Why does Hartree-Fock work so well?

Why does the Hartree-Fock method for electronic structure work so well for atoms? More specifically, why is the "correlation energy" a relatively small component of an atom's (ground state) ...
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20 views

Calculating surface charge in Thomas-Fermi layer

My understanding is that chemical potential at the surface of a bulk crystal is concentrated at, and would be described by, the Thomas-Fermi Layer (see Ad-atoms and underpotential): https://www....
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31 views

Irreducible representation of derivatives of diabatic electronic wave functions

My question regards the symmetry properties of the derivatives of diabatic electronic wavefunctions. I think the question goes somewhat beyond the standard group theoretical machinery taught in ...
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3answers
114 views

How to distinguish the $p_x$, $p_y$, $p_z$ orbitals when one can choose the $x-$, $y-$, and $z-$ axes arbitrary?

How to distinguish the $p_x$, $p_y$, $p_z$ orbitals since one could choose the $x-$, $y-$ and $z-$axes arbitrary? How could the can the wavefunctions that describe the probability of the presence of ...
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29 views

Widespread false formulation of Hunds 1. rule

According to Wikpedia Hunds first rule says Hunds 1. rule, Wikipedia: For a given electron configuration, the term with maximum multiplicity ($2S+1$) has the lowest energy. I would formulate this ...
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43 views

Why would one think that a solution of the time-independent Schrödinger equation is in the span of configuration state functions?

I am trying to understand why the hypothesis of configuration interaction methods is valid, i.e. I want to understand why one would think that an $N$-body wave function would be in the span of ...
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18 views

Atomic density derivative with respect to nuclear coordinates transformed to all space

Please show that the derivative of some atomic density $\rho_{I}$ with respect to its nuclear coordinate $R_{I}$ can be expressed in terms of its electronic coordinate $|\textbf{r - R}_I|$ $ \frac{\...
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1answer
36 views

Hydrogen bonding under quantum mechanics

I know that Fermi-Dirac statistics can be used to account for covalent bonding, but how does quantum mechanics explain hydrogen bonding?
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63 views

How to interpret Hamiltonian in terms of its matrix representation

I am reading a research paper (A Theoretical Analysis of Zero Field Splitting Parameters of Mn2+ Doped Diglycine Calcium Chloride Tetrahydrate) where they state the Hamiltonian term: $$H=\frac{F}{180}\...
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19 views

Is the $g$-tensor describing the Zeeman effect for molecules always diagonalizable?

The Zeeman splitting of a molecule can be described through the $g$-tensor, which couples the magnetic field to the angular momentum of the molecule. Is the $g$-tensor always diagonalizable?
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1answer
24 views

Degree of kinetic energy component in Hamiltonian for any molecule

In reading "Density functional theory of atoms and molecules" by Parr and Yang, I was not sure what is meant by this sentence when the Virial theorem was introduced. Suppose I have a ...
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1answer
135 views

Casimir effect evidence

How does the attraction between two metal plates support a new effect (or force)? Isn't it expected that two plates attract each other due to the London dispersion? If so, how does the experiment ...
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1answer
45 views

Hybrid Orbitals

https://glossary.periodni.com/glossary.php?page=41&en=high+fructose pictures like the ones in this article make no sense to me. I understand that we can take solutions to the Schrödinger equation ...
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61 views

Why do elements want to mimic Nobel gasses so much? [duplicate]

Why is the octet rule true? How can electrons even stay around nuclei with lesser number of protons?
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88 views

How does the Pauli Exclusion principle explain the incompressibility of metals?

The Pauli Exclusion principles states that no two identical fermions can have the same quantum state. In my lecture notes, it is mentioned that this principle helps us explain the fact that metals are ...
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37 views

Expression and explanation of quantum mechanical harmonic oscillator

I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Quantum Mechanical Harmonic Oscillator, the author says the following: Fig. 2....
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67 views

Hamiltonian matrix elements involving ladder operators for spin-1 state

I am reading the Doctorate thesis 'Zero-Field Anisotropic Spin Hamiltonians in First-Row Transition Metal Complexes: Theory, Models and Applications' (link: https://tel.archives-ouvertes.fr/tel-...
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26 views

Two descriptions of Valence Bond Theory

I am trying to understand theoretically Valence Bond Theory from the first principles of Quantum Mechanics and suitable approximations. I am a mathematician with shaky bases in Quantum Mechanics. ...
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1answer
112 views

Is the $1s^22s^22p^6$ atomic configuration lower in energy than the $1s^22s^22p^5$ atomic configuration?

I read that atoms in the first few rows of the periodic table gain or lose electrons to have 8 valence electrons so that they are energetically stable and has minimum energy. This means that an atom ...
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71 views

Interpretation of occupation numbers and creation-annihilation operators in strongly correlated systems

I hope I am not asking anything stupid, but I am having a hard time interpreting some (seemingly simple) results. The simplest approximate form of an $N$-electron wave function (w.f.) is a Slater-...
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1answer
51 views

Unitary Coupled Cluster Operator

In quantum computing, we always want to deal with unitary evolution operators. That's why the traditional definition of the Coupled Cluster ansatz is modified to the so-called Unitary Coupled Cluster, ...
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1answer
92 views

Benzene ground state

I’m currently studying my first course on Quantum Physics. Regarding the topic of Sommerfeld’s quantization rules, I’ve come across a problem where I was asked whether a benzene molecule would require ...
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34 views

Calculation of atomic spectrum

I need to calculate spectrum of Hg atom (wavelength and transition intensity), taking into account relativistic corrections. Can someone suggest a software or a package for atomic spectroscopy, that I ...
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3answers
207 views

What are the $sp^3$ orbital bond directions relative to a Cartesian reference frame?

When I try to search for this, I find images like below, but it is not clear to me what the actual bond directions are, i.e. the first one appears to be (0, 0, 1) but then I am not sure of the others.
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1answer
50 views

Quantitative contribution of kinetic and potential energies to the binding energy of the $\sigma$ orbital in $\text{H}_2$ or $\text{H}_2^+$

When a hydrogen molecule forms, 4.52 eV of energy is released, while for $\text{H}_2^+$ the binding energy is 2.77 eV. Such a binding energy is the difference of energies that have four terms in them: ...
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4answers
287 views

Why does orbital overlap cause attraction?

I have been taught that when orbitals overlap as in $\sigma$ and $π$ bonds, the formation of a bond (which is basically an attraction) takes place. Why does this cause attraction, shouldn't they repel?...
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1answer
157 views

How to calculate the second-order pertubation in an electron gas?

This problem is from the book Quantum theory of many particles systems by Fetter & Walecka (1971), exercise 1.4. Problem discription: The Hamiltonian could be divided into $$H_0=\sum_\limits{\...
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238 views

Can you explain DFT and TDDFT functioning (math aside)?

I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT and Time-Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...
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35 views

Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?

Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity) Theoretical ...
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95 views

Is it the Coulomb force which acts between electron and protons creating chemical bonds?

When calculating forces on the atomic level, although Quantum mechanics makes the positions of charged particles"smeared out" is it the Coulomb force which is acting between smeared out electrons and ...

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